All reactions and manipulations were performed in the ambient atmosphere. The Schiff-based H₂L ligand was prepared by condensation with o-vanillin and hydrazine-2-carbohydrazide in methanol according to the literature (Chandrasekhar et al., 2013; Chen et al., 2016). Metal salts and other reagents were commercially available and used without further purification.

Synthesis of Gd₂(L)₂(NO₃)₂(H₂O)₂‧CH₃CN‧H₂O (1): a mixture of H₂L (0.1 mmol, 27.2 mg) and Gd(NO₃)₃·6H₂O (0.1 mmol, 45.7 mg) was dissolved in CH₃CN (5 ml) and CH₃OH (2.5 ml). After stirring for 5 min, pyridine (0.04 ml) was added and stirred for another 10 min. The solution was filtered and left to slowly evaporate. Well-shaped orange crystals were obtained after 1 week. Yield: 20 mg, 36% based on Gd. Elemental analysis (EA) calc. (%) for Gd₂C₃₀H₃₀N₁₂O₁₆, C: 31.91, H: 2.68, N: 14.89; found (%), C: 32.03, H: 2.61, N: 14.93.

{Gd₆(L)₆(CO₃)₂(CH₃OH)₂(H₂O)₃Cl}Cl‧4CH₃CN (2): a mixture of H₂L (0.2 mmol, 54.4 mg) and GdCl₃.6H₂O (0.2 mmol, 74.3 mg) was dissolved in CH₃CN (10 ml) and CH₃OH (5 ml). After stirring for 5 min, NaHCO₃ (0.2 mmol, 33.6 mg) was added and stirred for another 3 h. Well-shaped orange crystals were obtained after 1 week. Yield: 32 mg, 32% based on Gd. Elemental analysis (EA) calc. (%) for Gd₆C₉₀H₉₂N₂₈O₂₉Cl₂, C: 35.51, H: 3.05, N: 12.88; found (%), C: 35.72, H: 2.99, N: 12.92.

Gd₈(L)₈(CO₃)₄(H₂O)₈‧2H₂O (3): a mixture of H₂L (0.2 mmol, 13.6 mg) and GdCl₃.6H₂O (0.2 mmol, 18.6 mg) was dissolved in CH₃CN (5 ml) and CH₃OH (2.5 ml). After stirring for 5 min, NaCO₃ (0.2 mmol, 10.6 mg) was added and stirred for another 2 h. Well-shaped orange crystals were obtained after 1 week. Yield: 28 mg, 29% based on Gd. Elemental analysis (EA) calc. (%) for Gd₈C₁₀₈H₁₀₀N₃₂O₄₆, C: 33.78, H: 2.62, N: 11.67; found (%), C: 33.83, H: 2.51, N: 11.84.

The C, H, and N elemental analyses were performed using an Elementar Vario-EL CHNS elemental analyzer. The Fourier transform-infrared (FT-IR) spectra were carried out from KBr pellets in the range 4,000–400 cm⁻¹ using an EQUINOX 55 spectrometer. Powder X-ray diffraction (PXRD) patterns were performed using the Bruker D8 Advance diffractometer (Cu–Kα, λ = 1.54056 Å). Magnetic susceptibility measurements were measured with a Quantum Design MPMS-XL7 SQUID. Polycrystalline samples were embedded in vaseline to prevent torquing. Data were corrected for the diamagnetic contribution calculated from Pascal constants.

Suitable single crystals for 1–3 were selected for single-crystal X-ray diffraction analysis. Data were collected using a Rigaku Oxford diffractometer with a Mo–Kα radiation (λ = 0.71073 Å) at 120 K. The structures were solved by direct methods and refined by least-squares on F ² utilizing the SHELXTL program suite and Olex2 (Dolomanov et al., 2009; Sheldrick, 2015a,b). The hydrogen atoms were set in calculated positions and refined as riding atoms with common fixed isotropic thermal parameters. EA was used to detect the content of C, H, and N atoms. Detailed information about the crystal data and structure refinements is summarized in Table 1. Selected bond lengths and angles of complexes 1–3 are listed in Supplementary Table S1–S3.

Complexes 1–3 are synthesized by the evolution method with H₂L and gadolinium salt in the solution of CH₃CN/CH₃OH (V ₁:V ₂ = 2:1) under the existence of alkali. The alkali is added to be conducive to protonate the ligand H₂L, which is beneficial to incorporate Gd^III ions. The H₂L ligand in all complexes is completely dehydrogenated adopting the μ ₂:η ²:η ¹ :η ¹ :η ¹ -mode (Scheme 1A), which is similar to the reported literature (Chandrasekhar et al., 2013; Chen et al., 2016; Zhang et al., 2017; Zhang  et al., 2016; Jiang et al., 2016).

Complex 1 is crystalized in the triclinic P-1 space group. As shown in Figure 1, the crystallography independent unit of 1 contains half of the molecule, including one Gd^III ion, one L₂ ^- ligand, one NO₃ ⁻ anion, and half of CH₃CN and H₂O molecules. The metallic Gd^III ions (Gd1 and Gd1A) are surrounded by two L₂ ^- ligands using the aforementioned mode, two NO₃ ⁻ anions and two H₂O molecules located above and below the plane, respectively. The average bond lengths of Gd-O and Gd-N are 2.379 (5) Å and 2.460 (5) Å (Supplementary Table S1), respectively, which are in accordance with those of the reported Gd-based complexes (Chen et al., 1995; Zhao et al., 2017; Mayans and Escuer, 2021; Ren et al., 2021). In complex 1, the Gd ion is seven-coordinated to form a capped trigonal prism, which is confirmed by CShM calculations (Alvarez et al., 2005; Casanova et al., 2005) (Supplementary Figure S1, Supplementary Table S4).

Complex 2 crystalizes in the same space group as complex 1, and the asymmetric unit comprises the whole molecule with six crystallographically independent Gd^III ions (Figure 2A). The six Gd ions are held together to form a {Gd₆} triangular prism metallic skeleton (Figure 2B). Therein, three Gd ions in the plane (Gd1, Gd2, and Gd3 or Gd4, Gd5, and Gd6) contribute a triangular configuration, which are bridged by one CO₃ ^2- anion in μ ₃-η ²:η ²:η ²-mode (Scheme 1B). The two triangular metallic skeletons are then linked together by six μ ₂-O bridges from ligands.

All Gd ions are eight coordinated, showing two kinds of coordination geometry confirmed by CShM calculations (Alvarez et al., 2005; Casanova et al., 2005) (Supplementary Table S5). The Gd1, Gd2, Gd3, Gd5, and Gd6 ions are in {O₆N₂} environment with six O atoms and two N atoms from two chelated L^2- ligands, one CO₃ ^2- anion and one CH₃OH/H₂O molecule, which display a biaugmented trigonal prism configuration (Supplementary Figure S2). The average Gd-O and Gd-N distances are 2.352 (4) Å and 2.475 (4) Å, respectively (Supplementary Table S2), which are consistent with those reported Gd-based complexes (Chen et al., 1995; Zhao et al., 2017; Mayans and Escuer, 2021; Ren et al., 2021). However, Gd4 has triangular dodecahedron coordination geometry and is located in an {O₅N₂Cl} environment with five O and two N atoms from two chelated L^2- ligands and one Cl⁻ anion. The bond length of Gd4-Cl1 is 2.746 (1) Å, which is longer than that of Gd-O and Gd-N.

For complex 3, the synthetic method is the same as complex 2; except NaHCO₃ was used in place of Na₂CO₃. Surprisingly, complex 3 possesses an octa-nuclearity structure, which crystalizes in the triclinic P-1 space group. The asymmetric unit consists of a completed molecule, and there are eight crystallographically independent Gd atoms in the molecular structure (Figure 3A). As shown in Figure 3B, the eight Gd^III ions contribute to a cubic trapezoid metallic core. Gd1, Gd4, Gd5, and Gd8 ions lie in the four vertices of the plane below the cubic trapezoid, while Gd2, Gd3, Gd6, and Gd7 ions situate in the upper plane. The metallic core is held together by four CO₃ ^2- anions in μ ₃-η ²:η ²:η ¹ -mode (Scheme 1C). The periphery of the metal core is ligated by eight L^2- ligands, eight H₂O molecules, and two lattice H₂O molecules.

There are two coordination numbers of Gd^III ions in complex 3 (Supplementary Figure S3). Gd1, Gd3, Gd5, and Gd7 are eight-coordinated ions in {O₆N₂} donor set from two L^2- ligands, two CO₃ ^2- anions, and one H₂O molecule, while Gd2, Gd4, Gd6, and Gd8 ions are nine-coordinated in the {O₇N₂} donor set. The difference between the two kinds of Gd ions is the diverse coordination modes of the CO₃ ^2- anion. There is only one coordination bond of O atom in CO₃ ^2- anion, which is adopted in Gd1, Gd3, Gd5, and Gd7 ions. For Gd2, Gd4, Gd6, and Gd8 ions, the bonding mode of the CO₃ ^2- anion is adopted in the bidentate mode. The eight metal ions exhibit three coordination geometries: biaugmented trigonal prism (Gd1), triangular dodecahedron (Gd3, Gd5, and Gd7), and muffin (Gd2, Gd4, Gd6, and Gd8) (Supplementary Tables S5,6). The average Gd-O distance is 2.361 (4) Å, which is shorter than that of Gd-N (2.564 (4) Å) lengths. The O/N-Gd-O/N angles are in the range of 60.99°–154.86°, which are in the normal range (Chen et al., 1995; Zhao et al., 2017; Mayans and Escuer, 2021; Ren et al., 2021).

It is worth mentioning that the use of different alkalis can affect the number of formed metal nuclearity. For the organic weak alkali triethylamine, which is used in complex 1, it only facilitates protonation of the ligand H₂L but is not involved in the final formation of complex 1. However, for complexes 2 and 3, the inorganic alkalis not only deprotonate the ligand but also participate in the construction of the molecules. Compared to NaHCO₃ in complex 2, the alkalinity of Na₂CO₃ is relatively strong. Moreover, mainly due to the degree of hydrolysis of carbonates being higher, there are more carbonate triangle skeletons in complex 3, making it easier to coordinate with Gd ions, thus forming an octa-nuclearity complex.

The FT-IR spectra of complexes 1–3 were acquired (v = 4,000–500 cm⁻¹), which are shown in Supplementary Figure S4. Powder X-ray diffraction (PXRD) measurements for complexes 1–3 were performed for the crystalline crystals (Supplementary Figure S5), and the experimental patterns are in good agreement with the simulated ones from the crystallographic data. The minor inconsistencies in the intensity and shape of the peaks indicate the phase purity of complexes 1–3.

The direct current magnetic susceptibilities of complexes 1–3 were studied for polycrystalline samples in the temperature range of 2–300 K at an external magnetic field of 1000 Oe (Figure 4A). At room temperature, the χ _M T values of complexes 1–3 are 15.77, 47.16, and 62.81 cm³ K mol⁻¹, respectively, which is in good agreement with the expected spin-only values (Gd^III ion: 7.875 cm³ K mol⁻¹, g = 2). Upon cooling, the χ _M T values in all cases stay essentially unchanged until approximately 25 K and then followed by an obvious decrease to the minimum values of 13.29, 38.46, and 58.30 cm³ K mol⁻¹, indicating antiferromagnetic interactions (Kahn et al., 2000). Fitting the curve of χ _M ⁻¹ vs. T with the Curie–Weiss Law (Figure 4B) gives the resulting C and θ values, which are listed in Supplementary Table S7. The negative θ values imply the presence of weak antiferromagnetic interaction within complexes 1–3.

The field dependence of the magnetization plots for complexes 1–3 was performed in the field range of 1–7 T at 2–8 K (Supplementary Figure S6). Magnetizations in all complexes are increased gradually at the entire field region, reaching saturation values of 13.81, 41.75, and 55.83 Nμ _B at 7 T and 2 K, respectively, close to the theoretical value (1: 14 Nμ _B; 2: 42 Nμ _B; 3: 56 Nμ _B). The reduced magnetization plots (M vs. HT ⁻¹) in all complexes are superposable due to the isotropic system (Supplementary Figure S7).

Due to the complicated systems in complexes 2 and 3, only complex 1 is attempted to analyze the magnetic interactions by using a simplified spin Hamiltonian with the PHI program (Eq. 1): H ^ G d − G d = − 2 J G d − G d S ^ G d 1 S ^ G d 2 . (1)

The best-fit parameters are J = -0.022 (2) cm⁻¹ and g = 1.98 (Figure 4A; Supplementary Figure S8). The negative J value confirms the antiferromagnetic interactions between the Gd^III ions, which is in accordance with the trend of the χ _M T product with cooling and the result of the Curie–Weiss Law.

The isothermal magnetization for complexes 1–3 was measured from 2 to 8 K in an applied DC field up to 7 T to calculate the magnetic entropy (-∆S _m) according to the Maxwell equation (Pecharsky and Gschneidner, 1999) (Eq. 2). It can be seen that the curves of -∆S _m of complexes 1–3 gradually increase with decreasing temperature and increasing of magnetic field without saturation, the maximum -∆S _m values are 25.05 J kg⁻¹ K⁻¹, 27.21 J kg⁻¹ K⁻¹, and 30.79 J kg⁻¹ K⁻¹ at 2 K, ∆H = 7 T, respectively (Figure 5). These values are smaller than the theoretical values of 34.57 J kg⁻¹ K⁻¹ for 1, 34.07 J kg⁻¹ K⁻¹ for 2, and 36.01 J kg⁻¹ K⁻¹ for 3, which are calculated using Eq 3, (n = 2, 6, and 8 for 1, 2, and 3, respectively; S = 7/2 and the R value is 8.314 J mol⁻¹ K⁻¹), owing to the existence of antiferromagnetic coupling. The maximum -∆S _m of 1 in di-nuclearity complex is among the highest observed to date for 4f clusters appeared at low temperature (Table 2). Although complexes 2 and 3 do not possess the highest -∆S _m values, they are still comparable in the same nuclear complexes. Δ S m ( T ) = ∫ 0 H [ ∂ M ( T , H ) / ∂ T ] H d H , (2) Δ S m ( T ) = n R   ln ( 2 S + 1 ) . (3)